Daily Papers

We consider learning representations (features) in the setting in which we have access to multiple unlabeled views of the data for learning while only one view is available for downstream tasks. Previous work on this problem has proposed several techniques based on deep neural networks, typically involving either autoencoder-like networks with a reconstruction objective or paired feedforward networks with a batch-style correlation-based objective. We analyze several techniques based on prior work, as well as new variants, and compare them empirically on image, speech, and text tasks. We find an advantage for correlation-based representation learning, while the best results on most tasks are obtained with our new variant, deep canonically correlated autoencoders (DCCAE). We also explore a stochastic optimization procedure for minibatch correlation-based objectives and discuss the time/performance trade-offs for kernel-based and neural network-based implementations.

Word Sense Disambiguation (WSD) has been widely evaluated using the semantic frameworks of WordNet, BabelNet, and the Oxford Dictionary of English. However, for the UCREL Semantic Analysis System (USAS) framework, no open extensive evaluation has been performed beyond lexical coverage or single language evaluation. In this work, we perform the largest semantic tagging evaluation of the rule based system that uses the lexical resources in the USAS framework covering five different languages using four existing datasets and one novel Chinese dataset. We create a new silver labelled English dataset, to overcome the lack of manually tagged training data, that we train and evaluate various mono and multilingual neural models in both mono and cross-lingual evaluation setups with comparisons to their rule based counterparts, and show how a rule based system can be enhanced with a neural network model. The resulting neural network models, including the data they were trained on, the Chinese evaluation dataset, and all of the code have been released as open resources.

Artificial neural networks have become a staple computing technique in many fields. Yet, they present fundamental differences with classical computing hardware in the way they process information. Photonic implementations of neural network architectures potentially offer fundamental advantages over their electronic counterparts in terms of speed, processing parallelism, scalability and energy efficiency. Scalable and high performance photonic neural networks (PNNs) have been demonstrated, yet they remain scarce. In this work, we study the performance of such a scalable, fully parallel and autonomous PNN based on a large area vertical-cavity surface-emitting laser (LA-VCSEL). We show how the performance varies with different physical parameters, namely, injection wavelength, injection power, and bias current. Furthermore, we link these physical parameters to the general computational measures of consistency and dimensionality. We present a general method of gauging dimensionality in high dimensional nonlinear systems subject to noise, which could be applied to many systems in the context of neuromorphic computing. Our work will inform future implementations of spatially multiplexed VCSEL PNNs.

Recognizing and categorizing human actions is an important task with applications in various fields such as human-robot interaction, video analysis, surveillance, video retrieval, health care system and entertainment industry. This thesis presents a novel computational approach for human action recognition through different implementations of multi-layer architectures based on artificial neural networks. Each system level development is designed to solve different aspects of the action recognition problem including online real-time processing, action segmentation and the involvement of objects. The analysis of the experimental results are illustrated and described in six articles. The proposed action recognition architecture of this thesis is composed of several processing layers including a preprocessing layer, an ordered vector representation layer and three layers of neural networks. It utilizes self-organizing neural networks such as Kohonen feature maps and growing grids as the main neural network layers. Thus the architecture presents a biological plausible approach with certain features such as topographic organization of the neurons, lateral interactions, semi-supervised learning and the ability to represent high dimensional input space in lower dimensional maps. For each level of development the system is trained with the input data consisting of consecutive 3D body postures and tested with generalized input data that the system has never met before. The experimental results of different system level developments show that the system performs well with quite high accuracy for recognizing human actions.

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

Recently, there has been an increasing interest in (supervised) learning with graph data, especially using graph neural networks. However, the development of meaningful benchmark datasets and standardized evaluation procedures is lagging, consequently hindering advancements in this area. To address this, we introduce the TUDataset for graph classification and regression. The collection consists of over 120 datasets of varying sizes from a wide range of applications. We provide Python-based data loaders, kernel and graph neural network baseline implementations, and evaluation tools. Here, we give an overview of the datasets, standardized evaluation procedures, and provide baseline experiments. All datasets are available at www.graphlearning.io. The experiments are fully reproducible from the code available at www.github.com/chrsmrrs/tudataset.

The entropic fictitious play (EFP) is a recently proposed algorithm that minimizes the sum of a convex functional and entropy in the space of measures -- such an objective naturally arises in the optimization of a two-layer neural network in the mean-field regime. In this work, we provide a concise primal-dual analysis of EFP in the setting where the learning problem exhibits a finite-sum structure. We establish quantitative global convergence guarantees for both the continuous-time and discrete-time dynamics based on properties of a proximal Gibbs measure introduced in Nitanda et al. (2022). Furthermore, our primal-dual framework entails a memory-efficient particle-based implementation of the EFP update, and also suggests a connection to gradient boosting methods. We illustrate the efficiency of our novel implementation in experiments including neural network optimization and image synthesis.

The new barrier mode in Apache Spark allows embedding distributed deep learning training as a Spark stage to simplify the distributed training workflow. In Spark, a task in a stage does not depend on any other tasks in the same stage, and hence it can be scheduled independently. However, several algorithms require more sophisticated inter-task communications, similar to the MPI paradigm. By combining distributed message passing (using asynchronous network IO), OpenJDK's new auto-vectorization and Spark's barrier execution mode, we can add non-map/reduce based algorithms, such as Cannon's distributed matrix multiplication to Spark. We document an efficient distributed matrix multiplication using Cannon's algorithm, which improves significantly on the performance of the existing MLlib implementation. Used within a barrier task, the algorithm described herein results in an up to 24 percent performance increase on a 10,000x10,000 square matrix with a significantly lower memory footprint. Applications of efficient matrix multiplication include, among others, accelerating the training and implementation of deep convolutional neural network based workloads, and thus such efficient algorithms can play a ground-breaking role in faster, more efficient execution of even the most complicated machine learning tasks.

Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.

Fracture is one of the main causes of failure in engineering structures. Phase field methods coupled with adaptive mesh refinement (AMR) techniques have been widely used to model crack propagation due to their ease of implementation and scalability. However, phase field methods can still be computationally demanding making them unfeasible for high-throughput design applications. Machine learning (ML) models such as Graph Neural Networks (GNNs) have shown their ability to emulate complex dynamic problems with speed-ups orders of magnitude faster compared to high-fidelity simulators. In this work, we present a dynamic mesh-based GNN framework for emulating phase field simulations of crack propagation with AMR for different crack configurations. The developed framework - ADAPTive mesh-based graph neural network (ADAPT-GNN) - exploits the benefits of both ML methods and AMR by describing the graph representation at each time-step as the refined mesh itself. Using ADAPT-GNN, we predict the evolution of displacement fields and scalar damage field (or phase field) with high accuracy compared to conventional phase field fracture model. We also compute crack stress fields with high accuracy using the predicted displacements and phase field parameter. Finally, we observe speed up of 15-36x compared to serial execution of the phase field model.

Spiking Neural Networks (SNNs), the third generation NNs, have come under the spotlight for machine learning based applications due to their biological plausibility and reduced complexity compared to traditional artificial Deep Neural Networks (DNNs). These SNNs can be implemented with extreme energy efficiency on neuromorphic processors like the Intel Loihi research chip, and fed by event-based sensors, such as DVS cameras. However, DNNs with many layers can achieve relatively high accuracy on image classification and recognition tasks, as the research on learning rules for SNNs for real-world applications is still not mature. The accuracy results for SNNs are typically obtained either by converting the trained DNNs into SNNs, or by directly designing and training SNNs in the spiking domain. Towards the conversion from a DNN to an SNN, we perform a comprehensive analysis of such process, specifically designed for Intel Loihi, showing our methodology for the design of an SNN that achieves nearly the same accuracy results as its corresponding DNN. Towards the usage of the event-based sensors, we design a pre-processing method, evaluated for the DvsGesture dataset, which makes it possible to be used in the DNN domain. Hence, based on the outcome of the first analysis, we train a DNN for the pre-processed DvsGesture dataset, and convert it into the spike domain for its deployment on Intel Loihi, which enables real-time gesture recognition. The results show that our SNN achieves 89.64% classification accuracy and occupies only 37 Loihi cores. The source code for generating our experiments is available online at https://github.com/albertomarchisio/EfficientSNN.

The performance of Deep Neural Networks (DNNs) keeps elevating in recent years with increasing network depth and width. To enable DNNs on edge devices like mobile phones, researchers proposed several network compression methods including pruning, quantization and factorization. Among the factorization-based approaches, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank decomposition; however, small approximation errors in parameters can ripple a large prediction loss. As a result, performance usually drops significantly and a sophisticated fine-tuning is required to recover accuracy. We argue that it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training. We propose Trained Rank Pruning (TRP), which iterates low rank approximation and training. TRP maintains the capacity of original network while imposes low-rank constraints during training. A stochastic sub-gradient descent optimized nuclear regularization is utilized to further encourage low rank in TRP. The TRP trained network has low-rank structure in nature, and can be approximated with negligible performance loss, eliminating fine-tuning after low rank approximation. The methods are comprehensively evaluated on CIFAR-10 and ImageNet, outperforming previous compression methods using low rank approximation. Code is available: https://github.com/yuhuixu1993/Trained-Rank-Pruning

The number of groups (g) in group convolution (GConv) is selected to boost the predictive performance of deep neural networks (DNNs) in a compute and parameter efficient manner. However, we show that naive selection of g in GConv creates an imbalance between the computational complexity and degree of data reuse, which leads to suboptimal energy efficiency in DNNs. We devise an optimum group size model, which enables a balance between computational cost and data movement cost, thus, optimize the energy-efficiency of DNNs. Based on the insights from this model, we propose an "energy-efficient group convolution" (E2GC) module where, unlike the previous implementations of GConv, the group size (G) remains constant. Further, to demonstrate the efficacy of the E2GC module, we incorporate this module in the design of MobileNet-V1 and ResNeXt-50 and perform experiments on two GPUs, P100 and P4000. We show that, at comparable computational complexity, DNNs with constant group size (E2GC) are more energy-efficient than DNNs with a fixed number of groups (FgGC). For example, on P100 GPU, the energy-efficiency of MobileNet-V1 and ResNeXt-50 is increased by 10.8% and 4.73% (respectively) when E2GC modules substitute the FgGC modules in both the DNNs. Furthermore, through our extensive experimentation with ImageNet-1K and Food-101 image classification datasets, we show that the E2GC module enables a trade-off between generalization ability and representational power of DNN. Thus, the predictive performance of DNNs can be optimized by selecting an appropriate G. The code and trained models are available at https://github.com/iithcandle/E2GC-release.

Shampoo is an online and stochastic optimization algorithm belonging to the AdaGrad family of methods for training neural networks. It constructs a block-diagonal preconditioner where each block consists of a coarse Kronecker product approximation to full-matrix AdaGrad for each parameter of the neural network. In this work, we provide a complete description of the algorithm as well as the performance optimizations that our implementation leverages to train deep networks at-scale in PyTorch. Our implementation enables fast multi-GPU distributed data-parallel training by distributing the memory and computation associated with blocks of each parameter via PyTorch's DTensor data structure and performing an AllGather primitive on the computed search directions at each iteration. This major performance enhancement enables us to achieve at most a 10% performance reduction in per-step wall-clock time compared against standard diagonal-scaling-based adaptive gradient methods. We validate our implementation by performing an ablation study on training ImageNet ResNet50, demonstrating Shampoo's superiority over standard training recipes with minimal hyperparameter tuning.

Both Minsky's "society of mind" and Schmidhuber's "learning to think" inspire diverse societies of large multimodal neural networks (NNs) that solve problems by interviewing each other in a "mindstorm." Recent implementations of NN-based societies of minds consist of large language models (LLMs) and other NN-based experts communicating through a natural language interface. In doing so, they overcome the limitations of single LLMs, improving multimodal zero-shot reasoning. In these natural language-based societies of mind (NLSOMs), new agents -- all communicating through the same universal symbolic language -- are easily added in a modular fashion. To demonstrate the power of NLSOMs, we assemble and experiment with several of them (having up to 129 members), leveraging mindstorms in them to solve some practical AI tasks: visual question answering, image captioning, text-to-image synthesis, 3D generation, egocentric retrieval, embodied AI, and general language-based task solving. We view this as a starting point towards much larger NLSOMs with billions of agents-some of which may be humans. And with this emergence of great societies of heterogeneous minds, many new research questions have suddenly become paramount to the future of artificial intelligence. What should be the social structure of an NLSOM? What would be the (dis)advantages of having a monarchical rather than a democratic structure? How can principles of NN economies be used to maximize the total reward of a reinforcement learning NLSOM? In this work, we identify, discuss, and try to answer some of these questions.

Neuromorphic models take inspiration from the human brain by adopting bio-plausible neuron models to build alternatives to traditional Machine Learning (ML) and Deep Learning (DL) solutions. The scarce availability of dedicated hardware able to actualize the emulation of brain-inspired computation, which is otherwise only simulated, yet still hinders the wide adoption of neuromorphic computing for edge devices and embedded systems. With this premise, we adopt the perspective of neuromorphic computing for conventional hardware and we present the L2MU, a natively neuromorphic Legendre Memory Unit (LMU) which entirely relies on Leaky Integrate-and-Fire (LIF) neurons. Specifically, the original recurrent architecture of LMU has been redesigned by modelling every constituent element with neural populations made of LIF or Current-Based (CuBa) LIF neurons. To couple neuromorphic computing and off-the-shelf edge devices, we equipped the L2MU with an input module for the conversion of real values into spikes, which makes it an encoding-free implementation of a Recurrent Spiking Neural Network (RSNN) able to directly work with raw sensor signals on non-dedicated hardware. As a use case to validate our network, we selected the task of Human Activity Recognition (HAR). We benchmarked our L2MU on smartwatch signals from hand-oriented activities, deploying it on three different commercial edge devices in compressed versions too. The reported results remark the possibility of considering neuromorphic models not only in an exclusive relationship with dedicated hardware but also as a suitable choice to work with common sensors and devices.

To plan and optimize energy storage demands that account for Li-ion battery aging dynamics, techniques need to be developed to diagnose battery internal states accurately and rapidly. This study seeks to reduce the computational resources needed to determine a battery's internal states by replacing physics-based Li-ion battery models -- such as the single-particle model (SPM) and the pseudo-2D (P2D) model -- with a physics-informed neural network (PINN) surrogate. The surrogate model makes high-throughput techniques, such as Bayesian calibration, tractable to determine battery internal parameters from voltage responses. This manuscript is the first of a two-part series that introduces PINN surrogates of Li-ion battery models for parameter inference (i.e., state-of-health diagnostics). In this first part, a method is presented for constructing a PINN surrogate of the SPM. A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals. The implementation is made available in a companion repository (https://github.com/NREL/pinnstripes). The techniques used to develop a PINN surrogate of the SPM are extended in Part II for the PINN surrogate for the P2D battery model, and explore the Bayesian calibration capabilities of both surrogates.

Potholes are common road hazards that is causing damage to vehicles and posing a safety risk to drivers. The introduction of Convolutional Neural Networks (CNNs) is widely used in the industry for object detection based on Deep Learning methods and has achieved significant progress in hardware improvement and software implementations. In this paper, a unique better algorithm is proposed to warrant the use of low-resolution cameras or low-resolution images and video feed for automatic pothole detection using Super Resolution (SR) through Super Resolution Generative Adversarial Networks (SRGANs). Then we have proceeded to establish a baseline pothole detection performance on low quality and high quality dashcam images using a You Only Look Once (YOLO) network, namely the YOLOv7 network. We then have illustrated and examined the speed and accuracy gained above the benchmark after having upscaling implementation on the low quality images.

We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover a network that can be expressed using a certain number of nonzero terms. Specifically, if there is a set of weights that uses at most s terms that can re-create the layer outputs from the layer inputs, we can find these weights from O(slog N/s) samples, where N is the input size. These theoretical results are similar to those for sparse regression using the Lasso, and our analysis uses some of the same recently-developed tools (namely recent results on the concentration of measure and convex analysis). Finally, we propose an algorithmic framework based on the alternating direction method of multipliers (ADMM), which allows a fast and simple implementation of Net-Trim for network pruning and compression.

In an era of information explosion, recommender systems are vital tools to deliver personalized recommendations for users. The key of recommender systems is to forecast users' future behaviors based on previous user-item interactions. Due to their strong expressive power of capturing high-order connectivities in user-item interaction data, recent years have witnessed a rising interest in leveraging Graph Neural Networks (GNNs) to boost the prediction performance of recommender systems. Nonetheless, classic Matrix Factorization (MF) and Deep Neural Network (DNN) approaches still play an important role in real-world large-scale recommender systems due to their scalability advantages. Despite the existence of GNN-acceleration solutions, it remains an open question whether GNN-based recommender systems can scale as efficiently as classic MF and DNN methods. In this paper, we propose a Linear-Time Graph Neural Network (LTGNN) to scale up GNN-based recommender systems to achieve comparable scalability as classic MF approaches while maintaining GNNs' powerful expressiveness for superior prediction accuracy. Extensive experiments and ablation studies are presented to validate the effectiveness and scalability of the proposed algorithm. Our implementation based on PyTorch is available.

Prior works on event-based optical flow estimation have investigated several gradient-based learning methods to train neural networks for predicting optical flow. However, they do not utilize the fast data rate of event data streams and rely on a spatio-temporal representation constructed from a collection of events over a fixed period of time (often between two grayscale frames). As a result, optical flow is only evaluated at a frequency much lower than the rate data is produced by an event-based camera, leading to a temporally sparse optical flow estimation. To predict temporally dense optical flow, we cast the problem as a sequential learning task and propose a training methodology to train sequential networks for continuous prediction on an event stream. We propose two types of networks: one focused on performance and another focused on compute efficiency. We first train long-short term memory networks (LSTMs) on the DSEC dataset and demonstrated 10x temporally dense optical flow estimation over existing flow estimation approaches. The additional benefit of having a memory to draw long temporal correlations back in time results in a 19.7% improvement in flow prediction accuracy of LSTMs over similar networks with no memory elements. We subsequently show that the inherent recurrence of spiking neural networks (SNNs) enables them to learn and estimate temporally dense optical flow with 31.8% lesser parameters than LSTM, but with a slightly increased error. This demonstrates potential for energy-efficient implementation of fast optical flow prediction using SNNs.

In this paper, we propose a learning rule based on a back-propagation (BP) algorithm that can be applied to a hardware-based deep neural network (HW-DNN) using electronic devices that exhibit discrete and limited conductance characteristics. This adaptive learning rule, which enables forward, backward propagation, as well as weight updates in hardware, is helpful during the implementation of power-efficient and high-speed deep neural networks. In simulations using a three-layer perceptron network, we evaluate the learning performance according to various conductance responses of electronic synapse devices and weight-updating methods. It is shown that the learning accuracy is comparable to that obtained when using a software-based BP algorithm when the electronic synapse device has a linear conductance response with a high dynamic range. Furthermore, the proposed unidirectional weight-updating method is suitable for electronic synapse devices which have nonlinear and finite conductance responses. Because this weight-updating method can compensate the demerit of asymmetric weight updates, we can obtain better accuracy compared to other methods. This adaptive learning rule, which can be applied to full hardware implementation, can also compensate the degradation of learning accuracy due to the probable device-to-device variation in an actual electronic synapse device.

Predictor-based methods have substantially enhanced Neural Architecture Search (NAS) optimization. The efficacy of these predictors is largely influenced by the method of encoding neural network architectures. While traditional encodings used an adjacency matrix describing the graph structure of a neural network, novel encodings embrace a variety of approaches from unsupervised pretraining of latent representations to vectors of zero-cost proxies. In this paper, we categorize and investigate neural encodings from three main types: structural, learned, and score-based. Furthermore, we extend these encodings and introduce unified encodings, that extend NAS predictors to multiple search spaces. Our analysis draws from experiments conducted on over 1.5 million neural network architectures on NAS spaces such as NASBench-101 (NB101), NB201, NB301, Network Design Spaces (NDS), and TransNASBench-101. Building on our study, we present our predictor FLAN: Flow Attention for NAS. FLAN integrates critical insights on predictor design, transfer learning, and unified encodings to enable more than an order of magnitude cost reduction for training NAS accuracy predictors. Our implementation and encodings for all neural networks are open-sourced at https://github.com/abdelfattah-lab/flan_nas{https://github.com/abdelfattah-lab/flan\_nas}.

Human Activity Recognition (HAR) is a relevant inference task in many mobile applications. State-of-the-art HAR at the edge is typically achieved with lightweight machine learning models such as decision trees and Random Forests (RFs), whereas deep learning is less common due to its high computational complexity. In this work, we propose a novel implementation of HAR based on deep neural networks, and precisely on Binary Neural Networks (BNNs), targeting low-power general purpose processors with a RISC-V instruction set. BNNs yield very small memory footprints and low inference complexity, thanks to the replacement of arithmetic operations with bit-wise ones. However, existing BNN implementations on general purpose processors impose constraints tailored to complex computer vision tasks, which result in over-parametrized models for simpler problems like HAR. Therefore, we also introduce a new BNN inference library, which targets ultra-compact models explicitly. With experiments on a single-core RISC-V processor, we show that BNNs trained on two HAR datasets obtain higher classification accuracy compared to a state-of-the-art baseline based on RFs. Furthermore, our BNN reaches the same accuracy of a RF with either less memory (up to 91%) or more energy-efficiency (up to 70%), depending on the complexity of the features extracted by the RF.

Machine learning, particularly in the form of deep learning, has driven most of the recent fundamental developments in artificial intelligence. Deep learning is based on computational models that are, to a certain extent, bio-inspired, as they rely on networks of connected simple computing units operating in parallel. Deep learning has been successfully applied in areas such as object/pattern recognition, speech and natural language processing, self-driving vehicles, intelligent self-diagnostics tools, autonomous robots, knowledgeable personal assistants, and monitoring. These successes have been mostly supported by three factors: availability of vast amounts of data, continuous growth in computing power, and algorithmic innovations. The approaching demise of Moore's law, and the consequent expected modest improvements in computing power that can be achieved by scaling, raise the question of whether the described progress will be slowed or halted due to hardware limitations. This paper reviews the case for a novel beyond CMOS hardware technology, memristors, as a potential solution for the implementation of power-efficient in-memory computing, deep learning accelerators, and spiking neural networks. Central themes are the reliance on non-von-Neumann computing architectures and the need for developing tailored learning and inference algorithms. To argue that lessons from biology can be useful in providing directions for further progress in artificial intelligence, we briefly discuss an example based reservoir computing. We conclude the review by speculating on the big picture view of future neuromorphic and brain-inspired computing systems.

Neural Architecture Search (NAS) algorithms automate the task of finding optimal deep learning architectures given an initial search space of possible operations. Developing these search spaces is usually a manual affair with pre-optimized search spaces being more efficient, rather than searching from scratch. In this paper we present a new framework called Neural Architecture Type System (NeuralArTS) that categorizes the infinite set of network operations in a structured type system. We further demonstrate how NeuralArTS can be applied to convolutional layers and propose several future directions.

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs

In this paper, we introduce a novel layer designed to be used as the output of pre-trained neural networks in the context of classification. Based on Associative Memories, this layer can help design Deep Neural Networks which support incremental learning and that can be (partially) trained in real time on embedded devices. Experiments on the ImageNet dataset and other different domain specific datasets show that it is possible to design more flexible and faster-to-train Neural Networks at the cost of a slight decrease in accuracy.

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.

We present a neural network architecture and training method designed to enable very rapid training and low implementation complexity. Due to its training speed and very few tunable parameters, the method has strong potential for applications requiring frequent retraining or online training. The approach is characterized by (a) convolutional filters based on biologically inspired visual processing filters, (b) randomly-valued classifier-stage input weights, (c) use of least squares regression to train the classifier output weights in a single batch, and (d) linear classifier-stage output units. We demonstrate the efficacy of the method by applying it to image classification. Our results match existing state-of-the-art results on the MNIST (0.37% error) and NORB-small (2.2% error) image classification databases, but with very fast training times compared to standard deep network approaches. The network's performance on the Google Street View House Number (SVHN) (4% error) database is also competitive with state-of-the art methods.

The weight matrix (WM) of a neural network (NN) is its program. The programs of many traditional NNs are learned through gradient descent in some error function, then remain fixed. The WM of a self-referential NN, however, can keep rapidly modifying all of itself during runtime. In principle, such NNs can meta-learn to learn, and meta-meta-learn to meta-learn to learn, and so on, in the sense of recursive self-improvement. While NN architectures potentially capable of implementing such behaviour have been proposed since the '90s, there have been few if any practical studies. Here we revisit such NNs, building upon recent successes of fast weight programmers and closely related linear Transformers. We propose a scalable self-referential WM (SRWM) that learns to use outer products and the delta update rule to modify itself. We evaluate our SRWM in supervised few-shot learning and in multi-task reinforcement learning with procedurally generated game environments. Our experiments demonstrate both practical applicability and competitive performance of the proposed SRWM. Our code is public.

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current formulations of such networks only the parameters of the neural modules and/or the order of their execution is learned. In this work, we further expand this approach and also learn the underlying internal structure of modules in terms of the ordering and combination of simple and elementary arithmetic operators. Our results show that one is indeed able to simultaneously learn both internal module structure and module sequencing without extra supervisory signals for module execution sequencing. With this approach, we report performance comparable to models using hand-designed modules.

We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop. Our input sequence acts as a punchcard, consisting of instructions and memory for data read/writes. We demonstrate that a constant number of encoder layers can emulate basic computing blocks, including embedding edit operations, non-linear functions, function calls, program counters, and conditional branches. Using these building blocks, we emulate a small instruction-set computer. This allows us to map iterative algorithms to programs that can be executed by a looped, 13-layer transformer. We show how this transformer, instructed by its input, can emulate a basic calculator, a basic linear algebra library, and in-context learning algorithms that employ backpropagation. Our work highlights the versatility of the attention mechanism, and demonstrates that even shallow transformers can execute full-fledged, general-purpose programs.

In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the i-th neuron in a nonlinear operator layer is defined by mathcal O_i(u) = sigmaleft( sum_j mathcal W_{ij} u + mathcal B_{ij}right). Here, mathcal W_{ij} denotes the bounded linear operator connecting j-th input neuron to i-th output neuron, and the bias mathcal B_{ij} takes the form of a function rather than a scalar. Given its new universal approximation property, the efficient parameterization of the bounded linear operators between two neurons (Banach spaces) plays a critical role. As a result, we introduce MgNO, utilizing multigrid structures to parameterize these linear operators between neurons. This approach offers both mathematical rigor and practical expressivity. Additionally, MgNO obviates the need for conventional lifting and projecting operators typically required in previous neural operators. Moreover, it seamlessly accommodates diverse boundary conditions. Our empirical observations reveal that MgNO exhibits superior ease of training compared to other CNN-based models, while also displaying a reduced susceptibility to overfitting when contrasted with spectral-type neural operators. We demonstrate the efficiency and accuracy of our method with consistently state-of-the-art performance on different types of partial differential equations (PDEs).

We show the formal equivalence of linearised self-attention mechanisms and fast weight controllers from the early '90s, where a ``slow" neural net learns by gradient descent to program the ``fast weights" of another net through sequences of elementary programming instructions which are additive outer products of self-invented activation patterns (today called keys and values). Such Fast Weight Programmers (FWPs) learn to manipulate the contents of a finite memory and dynamically interact with it. We infer a memory capacity limitation of recent linearised softmax attention variants, and replace the purely additive outer products by a delta rule-like programming instruction, such that the FWP can more easily learn to correct the current mapping from keys to values. The FWP also learns to compute dynamically changing learning rates. We also propose a new kernel function to linearise attention which balances simplicity and effectiveness. We conduct experiments on synthetic retrieval problems as well as standard machine translation and language modelling tasks which demonstrate the benefits of our methods.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: https://github.com/jwyyy/AdaFNN.

Neural networks can approximate complex functions, but they struggle to perform exact arithmetic operations over real numbers. The lack of inductive bias for arithmetic operations leaves neural networks without the underlying logic necessary to extrapolate on tasks such as addition, subtraction, and multiplication. We present two new neural network components: the Neural Addition Unit (NAU), which can learn exact addition and subtraction; and the Neural Multiplication Unit (NMU) that can multiply subsets of a vector. The NMU is, to our knowledge, the first arithmetic neural network component that can learn to multiply elements from a vector, when the hidden size is large. The two new components draw inspiration from a theoretical analysis of recently proposed arithmetic components. We find that careful initialization, restricting parameter space, and regularizing for sparsity is important when optimizing the NAU and NMU. Our proposed units NAU and NMU, compared with previous neural units, converge more consistently, have fewer parameters, learn faster, can converge for larger hidden sizes, obtain sparse and meaningful weights, and can extrapolate to negative and small values.

Linear recurrent neural networks (LRNNs) provide a structured approach to sequence modeling that bridges classical linear dynamical systems and modern deep learning, offering both expressive power and theoretical guarantees on stability and trainability. In recent years, multiple LRNN-based architectures have been proposed, each introducing distinct parameterizations, discretization schemes, and implementation constraints. However, existing implementations are fragmented across different software frameworks, often rely on framework-specific optimizations, and in some cases require custom CUDA kernels or lack publicly available code altogether. As a result, using, comparing, or extending LRNNs requires substantial implementation effort. To address this, we introduce lrnnx, a unified software library that implements several modern LRNN architectures under a common interface. The library exposes multiple levels of control, allowing users to work directly with core components or higher-level model abstractions. lrnnx aims to improve accessibility, reproducibility, and extensibility of LRNN research and applications. We make our code available under a permissive MIT license.

This paper aims to understand how neural networks learn algorithmic reasoning by addressing two questions: How faithful are learned algorithms when they are effective, and why do neural networks fail to learn effective algorithms otherwise? To answer these questions, we use neural compilation, a technique that directly encodes a source algorithm into neural network parameters, enabling the network to compute the algorithm exactly. This enables comparison between compiled and conventionally learned parameters, intermediate vectors, and behaviors. This investigation is crucial for developing neural networks that robustly learn complexalgorithms from data. Our analysis focuses on graph neural networks (GNNs), which are naturally aligned with algorithmic reasoning tasks, specifically our choices of BFS, DFS, and Bellman-Ford, which cover the spectrum of effective, faithful, and ineffective learned algorithms. Commonly, learning algorithmic reasoning is framed as induction over synthetic data, where a parameterized model is trained on inputs, traces, and outputs produced by an underlying ground truth algorithm. In contrast, we introduce a neural compilation method for GNNs, which sets network parameters analytically, bypassing training. Focusing on GNNs leverages their alignment with algorithmic reasoning, extensive algorithmic induction literature, and the novel application of neural compilation to GNNs. Overall, this paper aims to characterize expressability-trainability gaps - a fundamental shortcoming in learning algorithmic reasoning. We hypothesize that inductive learning is most effective for parallel algorithms contained within the computational class NC.

Neural architecture search (NAS) finds high performing networks for a given task. Yet the results of NAS are fairly prosaic; they did not e.g. create a shift from convolutional structures to transformers. This is not least because the search spaces in NAS often aren't diverse enough to include such transformations a priori. Instead, for NAS to provide greater potential for fundamental design shifts, we need a novel expressive search space design which is built from more fundamental operations. To this end, we introduce einspace, a search space based on a parameterised probabilistic context-free grammar. Our space is versatile, supporting architectures of various sizes and complexities, while also containing diverse network operations which allow it to model convolutions, attention components and more. It contains many existing competitive architectures, and provides flexibility for discovering new ones. Using this search space, we perform experiments to find novel architectures as well as improvements on existing ones on the diverse Unseen NAS datasets. We show that competitive architectures can be obtained by searching from scratch, and we consistently find large improvements when initialising the search with strong baselines. We believe that this work is an important advancement towards a transformative NAS paradigm where search space expressivity and strategic search initialisation play key roles.

Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this thesis we build a category-theoretic formalism around a class of neural networks exemplified by CycleGAN. CycleGAN is a collection of neural networks, closed under composition, whose inductive bias is increased by enforcing composition invariants, i.e. cycle-consistencies. Inspired by Functorial Data Migration, we specify the interconnection of these networks using a categorical schema, and network instances as set-valued functors on this schema. We also frame neural network architectures, datasets, models, and a number of other concepts in a categorical setting and thus show a special class of functors, rather than functions, can be learned using gradient descent. We use the category-theoretic framework to conceive a novel neural network architecture whose goal is to learn the task of object insertion and object deletion in images with unpaired data. We test the architecture on three different datasets and obtain promising results.

Over the past few years, neural networks have re-emerged as powerful machine-learning models, yielding state-of-the-art results in fields such as image recognition and speech processing. More recently, neural network models started to be applied also to textual natural language signals, again with very promising results. This tutorial surveys neural network models from the perspective of natural language processing research, in an attempt to bring natural-language researchers up to speed with the neural techniques. The tutorial covers input encoding for natural language tasks, feed-forward networks, convolutional networks, recurrent networks and recursive networks, as well as the computation graph abstraction for automatic gradient computation.

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very challenging. If successful, such architectures would be capable of performing a wide range of intriguing tasks, from adapting a pre-trained network to a new domain to editing objects represented as functions (INRs or NeRFs). As a first step towards this goal, we present here a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trained MLP and processes it using a composition of layers that are equivariant to the natural permutation symmetry of the MLP's weights: Changing the order of neurons in intermediate layers of the MLP does not affect the function it represents. We provide a full characterization of all affine equivariant and invariant layers for these symmetries and show how these layers can be implemented using three basic operations: pooling, broadcasting, and fully connected layers applied to the input in an appropriate manner. We demonstrate the effectiveness of our architecture and its advantages over natural baselines in a variety of learning tasks.

Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However, existing approaches either overlook the inherent permutation symmetry in the neural network or rely on intricate weight-sharing patterns to achieve equivariance, while ignoring the impact of the network architecture itself. In this work, we propose to represent neural networks as computational graphs of parameters, which allows us to harness powerful graph neural networks and transformers that preserve permutation symmetry. Consequently, our approach enables a single model to encode neural computational graphs with diverse architectures. We showcase the effectiveness of our method on a wide range of tasks, including classification and editing of implicit neural representations, predicting generalization performance, and learning to optimize, while consistently outperforming state-of-the-art methods. The source code is open-sourced at https://github.com/mkofinas/neural-graphs.

Neural networks can learn to represent and manipulate numerical information, but they seldom generalize well outside of the range of numerical values encountered during training. To encourage more systematic numerical extrapolation, we propose an architecture that represents numerical quantities as linear activations which are manipulated using primitive arithmetic operators, controlled by learned gates. We call this module a neural arithmetic logic unit (NALU), by analogy to the arithmetic logic unit in traditional processors. Experiments show that NALU-enhanced neural networks can learn to track time, perform arithmetic over images of numbers, translate numerical language into real-valued scalars, execute computer code, and count objects in images. In contrast to conventional architectures, we obtain substantially better generalization both inside and outside of the range of numerical values encountered during training, often extrapolating orders of magnitude beyond trained numerical ranges.

Neural networks have proven to be a highly effective tool for solving complex problems in many areas of life. Recently, their importance and practical usability have further been reinforced with the advent of deep learning. One of the important conditions for the success of neural networks is the choice of an appropriate activation function introducing non-linearity into the model. Many types of these functions have been proposed in the literature in the past, but there is no single comprehensive source containing their exhaustive overview. The absence of this overview, even in our experience, leads to redundancy and the unintentional rediscovery of already existing activation functions. To bridge this gap, our paper presents an extensive survey involving 400 activation functions, which is several times larger in scale than previous surveys. Our comprehensive compilation also references these surveys; however, its main goal is to provide the most comprehensive overview and systematization of previously published activation functions with links to their original sources. The secondary aim is to update the current understanding of this family of functions.

Multiple extensions of Recurrent Neural Networks (RNNs) have been proposed recently to address the difficulty of storing information over long time periods. In this paper, we experiment with the capacity of Neural Turing Machines (NTMs) to deal with these long-term dependencies on well-balanced strings of parentheses. We show that not only does the NTM emulate a stack with its heads and learn an algorithm to recognize such words, but it is also capable of strongly generalizing to much longer sequences.

Neural networks adapt very well to distributed and continuous representations, but struggle to generalize from small amounts of data. Symbolic systems commonly achieve data efficient generalization by exploiting modularity to benefit from local and discrete features of a representation. These features allow symbolic programs to be improved one module at a time and to experience combinatorial growth in the values they can successfully process. However, it is difficult to design a component that can be used to form symbolic abstractions and which is adequately overparametrized to learn arbitrary high-dimensional transformations. I present Graph-based Symbolically Synthesized Neural Networks (G-SSNNs), a class of neural modules that operate on representations modified with synthesized symbolic programs to include a fixed set of local and discrete features. I demonstrate that the choice of injected features within a G-SSNN module modulates the data efficiency and generalization of baseline neural models, creating predictable patterns of both heightened and curtailed generalization. By training G-SSNNs, we also derive information about desirable semantics of symbolic programs without manual engineering. This information is compact and amenable to abstraction, but can also be flexibly recontextualized for other high-dimensional settings. In future work, I will investigate data efficient generalization and the transferability of learned symbolic representations in more complex G-SSNN designs based on more complex classes of symbolic programs. Experimental code and data are available at https://github.com/shlomenu/symbolically_synthesized_networks .

This paper introduces a structured memory which can be easily integrated into a neural network. The memory is very large by design and significantly increases the capacity of the architecture, by up to a billion parameters with a negligible computational overhead. Its design and access pattern is based on product keys, which enable fast and exact nearest neighbor search. The ability to increase the number of parameters while keeping the same computational budget lets the overall system strike a better trade-off between prediction accuracy and computation efficiency both at training and test time. This memory layer allows us to tackle very large scale language modeling tasks. In our experiments we consider a dataset with up to 30 billion words, and we plug our memory layer in a state-of-the-art transformer-based architecture. In particular, we found that a memory augmented model with only 12 layers outperforms a baseline transformer model with 24 layers, while being twice faster at inference time. We release our code for reproducibility purposes.

Neural operators, as an efficient surrogate model for learning the solutions of PDEs, have received extensive attention in the field of scientific machine learning. Among them, attention-based neural operators have become one of the mainstreams in related research. However, existing approaches overfit the limited training data due to the considerable number of parameters in the attention mechanism. To address this, we develop an orthogonal attention based on the eigendecomposition of the kernel integral operator and the neural approximation of eigenfunctions. The orthogonalization naturally poses a proper regularization effect on the resulting neural operator, which aids in resisting overfitting and boosting generalization. Experiments on six standard neural operator benchmark datasets comprising both regular and irregular geometries show that our method can outperform competing baselines with decent margins.

We introduce torchNTK, a python library to calculate the empirical neural tangent kernel (NTK) of neural network models in the PyTorch framework. We provide an efficient method to calculate the NTK of multilayer perceptrons. We compare the explicit differentiation implementation against autodifferentiation implementations, which have the benefit of extending the utility of the library to any architecture supported by PyTorch, such as convolutional networks. A feature of the library is that we expose the user to layerwise NTK components, and show that in some regimes a layerwise calculation is more memory efficient. We conduct preliminary experiments to demonstrate use cases for the software and probe the NTK.

Neural architecture search (NAS) automates the design process of high-performing architectures, but remains bottlenecked by expensive performance evaluation. Most existing studies that achieve faster evaluation are mostly tied to cell-based search spaces and graph encodings tailored to those individual search spaces, limiting their flexibility and scalability when applied to more expressive search spaces. In this work, we aim to close the gap of individual search space restrictions and search space dependent network representations. We present ONNX-Bench, a benchmark consisting of a collection of neural networks in a unified format based on ONNX files. ONNX-Bench includes all open-source NAS-bench-based neural networks, resulting in a total size of more than 600k {architecture, accuracy} pairs. This benchmark allows creating a shared neural network representation, ONNX-Net, able to represent any neural architecture using natural language descriptions acting as an input to a performance predictor. This text-based encoding can accommodate arbitrary layer types, operation parameters, and heterogeneous topologies, enabling a single surrogate to generalise across all neural architectures rather than being confined to cell-based search spaces. Experiments show strong zero-shot performance across disparate search spaces using only a small amount of pretraining samples, enabling the unprecedented ability to evaluate any neural network architecture instantly.

The ability to learn tasks in a sequential fashion is crucial to the development of artificial intelligence. Neural networks are not, in general, capable of this and it has been widely thought that catastrophic forgetting is an inevitable feature of connectionist models. We show that it is possible to overcome this limitation and train networks that can maintain expertise on tasks which they have not experienced for a long time. Our approach remembers old tasks by selectively slowing down learning on the weights important for those tasks. We demonstrate our approach is scalable and effective by solving a set of classification tasks based on the MNIST hand written digit dataset and by learning several Atari 2600 games sequentially.

Diagrams matter. Unfortunately, the deep learning community has no standard method for diagramming architectures. The current combination of linear algebra notation and ad-hoc diagrams fails to offer the necessary precision to understand architectures in all their detail. However, this detail is critical for faithful implementation, mathematical analysis, further innovation, and ethical assurances. I present neural circuit diagrams, a graphical language tailored to the needs of communicating deep learning architectures. Neural circuit diagrams naturally keep track of the changing arrangement of data, precisely show how operations are broadcast over axes, and display the critical parallel behavior of linear operations. A lingering issue with existing diagramming methods is the inability to simultaneously express the detail of axes and the free arrangement of data, which neural circuit diagrams solve. Their compositional structure is analogous to code, creating a close correspondence between diagrams and implementation. In this work, I introduce neural circuit diagrams for an audience of machine learning researchers. After introducing neural circuit diagrams, I cover a host of architectures to show their utility and breed familiarity. This includes the transformer architecture, convolution (and its difficult-to-explain extensions), residual networks, the U-Net, and the vision transformer. I include a Jupyter notebook that provides evidence for the close correspondence between diagrams and code. Finally, I examine backpropagation using neural circuit diagrams. I show their utility in providing mathematical insight and analyzing algorithms' time and space complexities.

Random Neural Networks (RNNs) are a class of Neural Networks (NNs) that can also be seen as a specific type of queuing network. They have been successfully used in several domains during the last 25 years, as queuing networks to analyze the performance of resource sharing in many engineering areas, as learning tools and in combinatorial optimization, where they are seen as neural systems, and also as models of neurological aspects of living beings. In this article we focus on their learning capabilities, and more specifically, we present a practical guide for using the RNN to solve supervised learning problems. We give a general description of these models using almost indistinctly the terminology of Queuing Theory and the neural one. We present the standard learning procedures used by RNNs, adapted from similar well-established improvements in the standard NN field. We describe in particular a set of learning algorithms covering techniques based on the use of first order and, then, of second order derivatives. We also discuss some issues related to these objects and present new perspectives about their use in supervised learning problems. The tutorial describes their most relevant applications, and also provides a large bibliography.

The Mixture of Experts architecture allows for outrageously large neural networks by scaling model parameter size independently from computational demand (FLOPs). However, current DNN frameworks cannot effectively support the dynamic data flow in Mixture of Experts, and implementations on top of these frameworks need to use workarounds that introduce significant overheads. To address the limitation of these frameworks, we present DynaMoE, a DNN library that uses dynamic recompilations to optimize and adapt the use of computational resources to the dynamic needs of Mixture of Experts models. Our evaluation shows that DynaMoE achieves a 1.8x speedup and supports 2.3x larger model sizes when compared to existing MoE systems, even when not using recompilations. We then present further optimizations enabled by dynamic recompilations that yield an additional 1.7x speedup while simultaneously reducing memory pressure and improving model quality.

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. However, those works developed architectures tailored to specific networks such as MLPs and CNNs without normalization layers, and generalizing such architectures to other types of networks can be challenging. In this work, we overcome these challenges by building new metanetworks - neural networks that take weights from other neural networks as input. Put simply, we carefully build graphs representing the input neural networks and process the graphs using graph neural networks. Our approach, Graph Metanetworks (GMNs), generalizes to neural architectures where competing methods struggle, such as multi-head attention layers, normalization layers, convolutional layers, ResNet blocks, and group-equivariant linear layers. We prove that GMNs are expressive and equivariant to parameter permutation symmetries that leave the input neural network functions unchanged. We validate the effectiveness of our method on several metanetwork tasks over diverse neural network architectures.

Neurosymbolic (NeSy) frameworks combine neural representations and learning with symbolic representations and reasoning. Combining the reasoning capacities, explainability, and interpretability of symbolic processing with the flexibility and power of neural computing allows us to solve complex problems with more reliability while being data-efficient. However, this recently growing topic poses a challenge to developers with its learning curve, lack of user-friendly tools, libraries, and unifying frameworks. In this paper, we characterize the technical facets of existing NeSy frameworks, such as the symbolic representation language, integration with neural models, and the underlying algorithms. A majority of the NeSy research focuses on algorithms instead of providing generic frameworks for declarative problem specification to leverage problem solving. To highlight the key aspects of Neurosymbolic modeling, we showcase three generic NeSy frameworks - DeepProbLog, Scallop, and DomiKnowS. We identify the challenges within each facet that lay the foundation for identifying the expressivity of each framework in solving a variety of problems. Building on this foundation, we aim to spark transformative action and encourage the community to rethink this problem in novel ways.

Developing Intelligent Systems involves artificial intelligence approaches including artificial neural networks. Here, we present a tutorial of Deep Neural Networks (DNNs), and some insights about the origin of the term "deep"; references to deep learning are also given. Restricted Boltzmann Machines, which are the core of DNNs, are discussed in detail. An example of a simple two-layer network, performing unsupervised learning for unlabeled data, is shown. Deep Belief Networks (DBNs), which are used to build networks with more than two layers, are also described. Moreover, examples for supervised learning with DNNs performing simple prediction and classification tasks, are presented and explained. This tutorial includes two intelligent pattern recognition applications: hand- written digits (benchmark known as MNIST) and speech recognition.

Self-Supervised Learning (SSL) has been shown to learn useful and information-preserving representations. Neural Networks (NNs) are widely applied, yet their weight space is still not fully understood. Therefore, we propose to use SSL to learn hyper-representations of the weights of populations of NNs. To that end, we introduce domain specific data augmentations and an adapted attention architecture. Our empirical evaluation demonstrates that self-supervised representation learning in this domain is able to recover diverse NN model characteristics. Further, we show that the proposed learned representations outperform prior work for predicting hyper-parameters, test accuracy, and generalization gap as well as transfer to out-of-distribution settings.

Language models have achieved impressive results in natural language processing tasks, but their ability to perform symbolic operations and arithmetic operations, remains limited, which attribute to their learn the rules implicitly from data. We explore how to incorporate compiled neural networks (CoNNs) which weight is specially designed, into the architecture of language models to enable the language model trained by gradient to obtain fully rule comprehension ability. The incorporation of compiled neural networks offers a promising direction for improving the performance of language models on compound tasks, particularly in areas that require a deeper comprehension of abstract rules beyond recognizing patterns in training data. Our method, which call "Neural Comprehension", helps language models achieve absolute accuracy in symbolic operations, thereby enhancing their ability for rule reasoning, symbolic reasoning, and arithmetic reasoning. Our code is publicly available at: https://github.com/WENGSYX/Neural-Comprehension.

Hopfield neural networks are a possible basis for modelling associative memory in living organisms. After summarising previous studies in the field, we take a new look at learning rules, exhibiting them as descent-type algorithms for various cost functions. We also propose several new cost functions suitable for learning. We discuss the role of biases (the external inputs) in the learning process in Hopfield networks. Furthermore, we apply Newtons method for learning memories, and experimentally compare the performances of various learning rules. Finally, to add to the debate whether allowing connections of a neuron to itself enhances memory capacity, we numerically investigate the effects of self coupling. Keywords: Hopfield Networks, associative memory, content addressable memory, learning rules, gradient descent, attractor networks

Deep feedforward and recurrent networks have achieved impressive results in many perception and language processing applications. This success is partially attributed to architectural innovations such as convolutional and long short-term memory networks. The main motivation for these architectural innovations is that they capture better domain knowledge, and importantly are easier to optimize than more basic architectures. Recently, more complex architectures such as Neural Turing Machines and Memory Networks have been proposed for tasks including question answering and general computation, creating a new set of optimization challenges. In this paper, we discuss a low-overhead and easy-to-implement technique of adding gradient noise which we find to be surprisingly effective when training these very deep architectures. The technique not only helps to avoid overfitting, but also can result in lower training loss. This method alone allows a fully-connected 20-layer deep network to be trained with standard gradient descent, even starting from a poor initialization. We see consistent improvements for many complex models, including a 72% relative reduction in error rate over a carefully-tuned baseline on a challenging question-answering task, and a doubling of the number of accurate binary multiplication models learned across 7,000 random restarts. We encourage further application of this technique to additional complex modern architectures.

Our understanding of the generalization capabilities of neural networks (NNs) is still incomplete. Prevailing explanations are based on implicit biases of gradient descent (GD) but they cannot account for the capabilities of models from gradient-free methods nor the simplicity bias recently observed in untrained networks. This paper seeks other sources of generalization in NNs. Findings. To understand the inductive biases provided by architectures independently from GD, we examine untrained, random-weight networks. Even simple MLPs show strong inductive biases: uniform sampling in weight space yields a very biased distribution of functions in terms of complexity. But unlike common wisdom, NNs do not have an inherent "simplicity bias". This property depends on components such as ReLUs, residual connections, and layer normalizations. Alternative architectures can be built with a bias for any level of complexity. Transformers also inherit all these properties from their building blocks. Implications. We provide a fresh explanation for the success of deep learning independent from gradient-based training. It points at promising avenues for controlling the solutions implemented by trained models.

Model compression is essential in the deployment of large Computer Vision models on embedded devices. However, static optimization techniques (e.g. pruning, quantization, etc.) neglect the fact that different inputs have different complexities, thus requiring different amount of computations. Dynamic Neural Networks allow to condition the number of computations to the specific input. The current literature on the topic is very extensive and fragmented. We present a comprehensive survey that synthesizes and unifies existing Dynamic Neural Networks research in the context of Computer Vision. Additionally, we provide a logical taxonomy based on which component of the network is adaptive: the output, the computation graph or the input. Furthermore, we argue that Dynamic Neural Networks are particularly beneficial in the context of Sensor Fusion for better adaptivity, noise reduction and information prioritization. We present preliminary works in this direction. We complement this survey with a curated repository listing all the surveyed papers, each with a brief summary of the solution and the code base when available: https://github.com/DTU-PAS/awesome-dynn-for-cv .

Neural networks are trained by choosing an architecture and training the parameters. The choice of architecture is often by trial and error or with Neural Architecture Search (NAS) methods. While NAS provides some automation, it often relies on discrete steps that optimize the architecture and then train the parameters. We introduce a novel neural network training framework that fundamentally transforms the process by learning architecture and parameters simultaneously with gradient descent. With the appropriate setting of the loss function, it can discover sparse and compact neural networks for given datasets. Central to our approach is a multi-scale encoder-decoder, in which the encoder embeds pairs of neural networks with similar functionalities close to each other (irrespective of their architectures and weights). To train a neural network with a given dataset, we randomly sample a neural network embedding in the embedding space and then perform gradient descent using our custom loss function, which incorporates a sparsity penalty to encourage compactness. The decoder generates a neural network corresponding to the embedding. Experiments demonstrate that our framework can discover sparse and compact neural networks maintaining a high performance.

The multi-modal nature of many vision problems calls for neural network architectures that can perform multiple tasks concurrently. Typically, such architectures have been handcrafted in the literature. However, given the size and complexity of the problem, this manual architecture exploration likely exceeds human design abilities. In this paper, we propose a principled approach, rooted in differentiable neural architecture search, to automatically define branching (tree-like) structures in the encoding stage of a multi-task neural network. To allow flexibility within resource-constrained environments, we introduce a proxyless, resource-aware loss that dynamically controls the model size. Evaluations across a variety of dense prediction tasks show that our approach consistently finds high-performing branching structures within limited resource budgets.

We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to produce a canonical representation of the data. These canonicalization functions can readily be plugged into non-equivariant backbone architectures. We offer explicit ways to implement them for many groups of interest. We show that this approach enjoys universality while providing interpretable insights. Our main hypothesis is that learning a neural network to perform canonicalization is better than using predefined heuristics. Our results show that learning the canonicalization function indeed leads to better results and that the approach achieves excellent performance in practice.

Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these alternatives have not yet been fully explored. We study the computational power of two of the most paradigmatic architectures exemplifying these mechanisms: the Transformer (Vaswani et al., 2017) and the Neural GPU (Kaiser & Sutskever, 2016). We show both models to be Turing complete exclusively based on their capacity to compute and access internal dense representations of the data. In particular, neither the Transformer nor the Neural GPU requires access to an external memory to become Turing complete. Our study also reveals some minimal sets of elements needed to obtain these completeness results.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Artificial Neural Networks are computational network models inspired by signal processing in the brain. These models have dramatically improved the performance of many learning tasks, including speech and object recognition. However, today's computing hardware is inefficient at implementing neural networks, in large part because much of it was designed for von Neumann computing schemes. Significant effort has been made to develop electronic architectures tuned to implement artificial neural networks that improve upon both computational speed and energy efficiency. Here, we propose a new architecture for a fully-optical neural network that, using unique advantages of optics, promises a computational speed enhancement of at least two orders of magnitude over the state-of-the-art and three orders of magnitude in power efficiency for conventional learning tasks. We experimentally demonstrate essential parts of our architecture using a programmable nanophotonic processor.

While neural networks have been remarkably successful in a wide array of applications, implementing them in resource-constrained hardware remains an area of intense research. By replacing the weights of a neural network with quantized (e.g., 4-bit, or binary) counterparts, massive savings in computation cost, memory, and power consumption are attained. To that end, we generalize a post-training neural-network quantization method, GPFQ, that is based on a greedy path-following mechanism. Among other things, we propose modifications to promote sparsity of the weights, and rigorously analyze the associated error. Additionally, our error analysis expands the results of previous work on GPFQ to handle general quantization alphabets, showing that for quantizing a single-layer network, the relative square error essentially decays linearly in the number of weights -- i.e., level of over-parametrization. Our result holds across a range of input distributions and for both fully-connected and convolutional architectures thereby also extending previous results. To empirically evaluate the method, we quantize several common architectures with few bits per weight, and test them on ImageNet, showing only minor loss of accuracy compared to unquantized models. We also demonstrate that standard modifications, such as bias correction and mixed precision quantization, further improve accuracy.

Toward combining inductive reasoning with perception abilities, we develop techniques for neurosymbolic program synthesis where perceptual input is first parsed by neural nets into a low-dimensional interpretable representation, which is then processed by a synthesized program. We explore several techniques for relaxing the problem and jointly learning all modules end-to-end with gradient descent: multitask learning; amortized inference; overparameterization; and a differentiable strategy for penalizing lengthy programs. Collectedly this toolbox improves the stability of gradient-guided program search, and suggests ways of learning both how to perceive input as discrete abstractions, and how to symbolically process those abstractions as programs.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.

We provide a new efficient version of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e.g., convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.

Artificial neural nets can represent and classify many types of data but are often tailored to particular applications -- e.g., for "fair" or "hierarchical" classification. Once an architecture has been selected, it is often difficult for humans to adjust models for a new task; for example, a hierarchical classifier cannot be easily transformed into a fair classifier that shields a protected field. Our contribution in this work is a new neural network architecture, the concept subspace network (CSN), which generalizes existing specialized classifiers to produce a unified model capable of learning a spectrum of multi-concept relationships. We demonstrate that CSNs reproduce state-of-the-art results in fair classification when enforcing concept independence, may be transformed into hierarchical classifiers, or even reconcile fairness and hierarchy within a single classifier. The CSN is inspired by existing prototype-based classifiers that promote interpretability.

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections to avoid the problem of vanishing gradients, they can be viewed as the numerical integration of a differential equation. In this extended abstract, we build upon this connection and propose a modification of the internal architecture of a transformer layer. The proposed model places the multi-head attention sublayer and the MLP sublayer parallel to each other. Our experiments show that this simple modification improves the performance of transformer networks in multiple tasks. Moreover, for the image classification task, we show that using neural ODE solvers with a sophisticated integration scheme further improves performance.

Recent advances in artificial neural networks for machine learning, and language modeling in particular, have established a family of recurrent neural network (RNN) architectures that, unlike conventional RNNs with vector-form hidden states, use two-dimensional (2D) matrix-form hidden states. Such 2D-state RNNs, known as Fast Weight Programmers (FWPs), can be interpreted as a neural network whose synaptic weights (called fast weights) dynamically change over time as a function of input observations, and serve as short-term memory storage; corresponding synaptic weight modifications are controlled or programmed by another network (the programmer) whose parameters are trained (e.g., by gradient descent). In this Primer, we review the technical foundations of FWPs, their computational characteristics, and their connections to transformers and state space models. We also discuss connections between FWPs and models of synaptic plasticity in the brain, suggesting a convergence of natural and artificial intelligence.

Originally inspired by neurobiology, deep neural network models have become a powerful tool of machine learning and artificial intelligence, where they are used to approximate functions and dynamics by learning from examples. Here we give a brief introduction to neural network models and deep learning for biologists. We introduce feedforward and recurrent networks and explain the expressive power of this modeling framework and the backpropagation algorithm for setting the parameters. Finally, we consider how deep neural networks might help us understand the brain's computations.

We propose a new frontier: Neural Computers (NCs) -- an emerging machine form that unifies computation, memory, and I/O in a learned runtime state. Unlike conventional computers, which execute explicit programs, agents, which act over external execution environments, and world models, which learn environment dynamics, NCs aim to make the model itself the running computer. Our long-term goal is the Completely Neural Computer (CNC): the mature, general-purpose realization of this emerging machine form, with stable execution, explicit reprogramming, and durable capability reuse. As an initial step, we study whether early NC primitives can be learned solely from collected I/O traces, without instrumented program state. Concretely, we instantiate NCs as video models that roll out screen frames from instructions, pixels, and user actions (when available) in CLI and GUI settings. These implementations show that learned runtimes can acquire early interface primitives, especially I/O alignment and short-horizon control, while routine reuse, controlled updates, and symbolic stability remain open. We outline a roadmap toward CNCs around these challenges. If overcome, CNCs could establish a new computing paradigm beyond today's agents, world models, and conventional computers.

In a conversation or a dialogue process, attention and intention play intrinsic roles. This paper proposes a neural network based approach that models the attention and intention processes. It essentially consists of three recurrent networks. The encoder network is a word-level model representing source side sentences. The intention network is a recurrent network that models the dynamics of the intention process. The decoder network is a recurrent network produces responses to the input from the source side. It is a language model that is dependent on the intention and has an attention mechanism to attend to particular source side words, when predicting a symbol in the response. The model is trained end-to-end without labeling data. Experiments show that this model generates natural responses to user inputs.

We introduce the concept of scalable neural network kernels (SNNKs), the replacements of regular feedforward layers (FFLs), capable of approximating the latter, but with favorable computational properties. SNNKs effectively disentangle the inputs from the parameters of the neural network in the FFL, only to connect them in the final computation via the dot-product kernel. They are also strictly more expressive, as allowing to model complicated relationships beyond the functions of the dot-products of parameter-input vectors. We also introduce the neural network bundling process that applies SNNKs to compactify deep neural network architectures, resulting in additional compression gains. In its extreme version, it leads to the fully bundled network whose optimal parameters can be expressed via explicit formulae for several loss functions (e.g. mean squared error), opening a possibility to bypass backpropagation. As a by-product of our analysis, we introduce the mechanism of the universal random features (or URFs), applied to instantiate several SNNK variants, and interesting on its own in the context of scalable kernel methods. We provide rigorous theoretical analysis of all these concepts as well as an extensive empirical evaluation, ranging from point-wise kernel estimation to Transformers' fine-tuning with novel adapter layers inspired by SNNKs. Our mechanism provides up to 5x reduction in the number of trainable parameters, while maintaining competitive accuracy.

Kolmogorov-Arnold Networks (KANs) have gained significant attention as an alternative to traditional multilayer perceptrons, with proponents claiming superior interpretability and performance through learnable univariate activation functions. However, recent systematic evaluations reveal substantial discrepancies between theoretical claims and empirical evidence. This critical assessment examines KANs' actual performance across diverse domains using fair comparison methodologies that control for parameters and computational costs. Our analysis demonstrates that KANs outperform MLPs only in symbolic regression tasks, while consistently underperforming in machine learning, computer vision, and natural language processing benchmarks. The claimed advantages largely stem from B-spline activation functions rather than architectural innovations, and computational overhead (1.36-100x slower) severely limits practical deployment. Furthermore, theoretical claims about breaking the "curse of dimensionality" lack rigorous mathematical foundation. We systematically identify the conditions under which KANs provide value versus traditional approaches, establish evaluation standards for future research, and propose a priority-based roadmap for addressing fundamental limitations. This work provides researchers and practitioners with evidence-based guidance for the rational adoption of KANs while highlighting critical research gaps that must be addressed for broader applicability.

Ranking models lie at the heart of research on information retrieval (IR). During the past decades, different techniques have been proposed for constructing ranking models, from traditional heuristic methods, probabilistic methods, to modern machine learning methods. Recently, with the advance of deep learning technology, we have witnessed a growing body of work in applying shallow or deep neural networks to the ranking problem in IR, referred to as neural ranking models in this paper. The power of neural ranking models lies in the ability to learn from the raw text inputs for the ranking problem to avoid many limitations of hand-crafted features. Neural networks have sufficient capacity to model complicated tasks, which is needed to handle the complexity of relevance estimation in ranking. Since there have been a large variety of neural ranking models proposed, we believe it is the right time to summarize the current status, learn from existing methodologies, and gain some insights for future development. In contrast to existing reviews, in this survey, we will take a deep look into the neural ranking models from different dimensions to analyze their underlying assumptions, major design principles, and learning strategies. We compare these models through benchmark tasks to obtain a comprehensive empirical understanding of the existing techniques. We will also discuss what is missing in the current literature and what are the promising and desired future directions.

Vertex centrality measures are a multi-purpose analysis tool, commonly used in many application environments to retrieve information and unveil knowledge from the graphs and network structural properties. However, the algorithms of such metrics are expensive in terms of computational resources when running real-time applications or massive real world networks. Thus, approximation techniques have been developed and used to compute the measures in such scenarios. In this paper, we demonstrate and analyze the use of neural network learning algorithms to tackle such task and compare their performance in terms of solution quality and computation time with other techniques from the literature. Our work offers several contributions. We highlight both the pros and cons of approximating centralities though neural learning. By empirical means and statistics, we then show that the regression model generated with a feedforward neural networks trained by the Levenberg-Marquardt algorithm is not only the best option considering computational resources, but also achieves the best solution quality for relevant applications and large-scale networks. Keywords: Vertex Centrality Measures, Neural Networks, Complex Network Models, Machine Learning, Regression Model

We present a novel neural network for processing sequences. The ByteNet is a one-dimensional convolutional neural network that is composed of two parts, one to encode the source sequence and the other to decode the target sequence. The two network parts are connected by stacking the decoder on top of the encoder and preserving the temporal resolution of the sequences. To address the differing lengths of the source and the target, we introduce an efficient mechanism by which the decoder is dynamically unfolded over the representation of the encoder. The ByteNet uses dilation in the convolutional layers to increase its receptive field. The resulting network has two core properties: it runs in time that is linear in the length of the sequences and it sidesteps the need for excessive memorization. The ByteNet decoder attains state-of-the-art performance on character-level language modelling and outperforms the previous best results obtained with recurrent networks. The ByteNet also achieves state-of-the-art performance on character-to-character machine translation on the English-to-German WMT translation task, surpassing comparable neural translation models that are based on recurrent networks with attentional pooling and run in quadratic time. We find that the latent alignment structure contained in the representations reflects the expected alignment between the tokens.

The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. This work develops a systematic approach to constructing matrix activation functions whose entries are generalized from ReLU. The activation is based on matrix-vector multiplications using only scalar multiplications and comparisons. The proposed activation functions depend on parameters that are trained along with the weights and bias vectors. Neural networks based on this approach are simple and efficient and are shown to be robust in numerical experiments.

While it is important to make implantable brain-machine interfaces (iBMI) wireless to increase patient comfort and safety, the trend of increased channel count in recent neural probes poses a challenge due to the concomitant increase in the data rate. Extracting information from raw data at the source by using edge computing is a promising solution to this problem, with integrated intention decoders providing the best compression ratio. Recent benchmarking efforts have shown recurrent neural networks to be the best solution. Spiking Neural Networks (SNN) emerge as a promising solution for resource efficient neural decoding while Long Short Term Memory (LSTM) networks achieve the best accuracy. In this work, we show that combining traditional signal processing techniques, namely signal filtering, with SNNs improve their decoding performance significantly for regression tasks, closing the gap with LSTMs, at little added cost. Results with different filters are shown with Bessel filters providing best performance. Two block-bidirectional Bessel filters have been used--one for low latency and another for high accuracy. Adding the high accuracy variant of the Bessel filters to the output of ANN, SNN and variants provided statistically significant benefits with maximum gains of approx 5% and 8% in R^2 for two SNN topologies (SNN\_Streaming and SNN\_3D). Our work presents state of the art results for this dataset and paves the way for decoder-integrated-implants of the future.

We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is differentiable end-to-end, allowing it to be efficiently trained with gradient descent. Preliminary results demonstrate that Neural Turing Machines can infer simple algorithms such as copying, sorting, and associative recall from input and output examples.

With the increasing number of new neural architecture designs and substantial existing neural architectures, it becomes difficult for the researchers to situate their contributions compared with existing neural architectures or establish the connections between their designs and other relevant ones. To discover similar neural architectures in an efficient and automatic manner, we define a new problem Neural Architecture Retrieval which retrieves a set of existing neural architectures which have similar designs to the query neural architecture. Existing graph pre-training strategies cannot address the computational graph in neural architectures due to the graph size and motifs. To fulfill this potential, we propose to divide the graph into motifs which are used to rebuild the macro graph to tackle these issues, and introduce multi-level contrastive learning to achieve accurate graph representation learning. Extensive evaluations on both human-designed and synthesized neural architectures demonstrate the superiority of our algorithm. Such a dataset which contains 12k real-world network architectures, as well as their embedding, is built for neural architecture retrieval.

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on cubic spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.

In this work we introduce malware detection from raw byte sequences as a fruitful research area to the larger machine learning community. Building a neural network for such a problem presents a number of interesting challenges that have not occurred in tasks such as image processing or NLP. In particular, we note that detection from raw bytes presents a sequence problem with over two million time steps and a problem where batch normalization appear to hinder the learning process. We present our initial work in building a solution to tackle this problem, which has linear complexity dependence on the sequence length, and allows for interpretable sub-regions of the binary to be identified. In doing so we will discuss the many challenges in building a neural network to process data at this scale, and the methods we used to work around them.

Designing neural networks typically relies on manual trial and error or a neural architecture search (NAS) followed by weight training. The former is time-consuming and labor-intensive, while the latter often discretizes architecture search and weight optimization. In this paper, we propose a fundamentally different approach that simultaneously optimizes both the architecture and the weights of a neural network. Our framework first trains a universal multi-scale autoencoder that embeds both architectural and parametric information into a continuous latent space, where functionally similar neural networks are mapped closer together. Given a dataset, we then randomly initialize a point in the embedding space and update it via gradient descent to obtain the optimal neural network, jointly optimizing its structure and weights. The optimization process incorporates sparsity and compactness penalties to promote efficient models. Experiments on synthetic regression tasks demonstrate that our method effectively discovers sparse and compact neural networks with strong performance.

Over the last decades, deep neural networks based-models became the dominant paradigm in machine learning. Further, the use of artificial neural networks in symbolic learning has been seen as increasingly relevant recently. To study the capabilities of neural networks in the symbolic AI domain, researchers have explored the ability of deep neural networks to learn mathematical constructions, such as addition and multiplication, logic inference, such as theorem provers, and even the execution of computer programs. The latter is known to be too complex a task for neural networks. Therefore, the results were not always successful, and often required the introduction of biased elements in the learning process, in addition to restricting the scope of possible programs to be executed. In this work, we will analyze the ability of neural networks to learn how to execute programs as a whole. To do so, we propose a different approach. Instead of using an imperative programming language, with complex structures, we use the Lambda Calculus (λ-Calculus), a simple, but Turing-Complete mathematical formalism, which serves as the basis for modern functional programming languages and is at the heart of computability theory. We will introduce the use of integrated neural learning and lambda calculi formalization. Finally, we explore execution of a program in λ-Calculus is based on reductions, we will show that it is enough to learn how to perform these reductions so that we can execute any program. Keywords: Machine Learning, Lambda Calculus, Neurosymbolic AI, Neural Networks, Transformer Model, Sequence-to-Sequence Models, Computational Models

Harnessing the statistical power of neural networks to perform language understanding and symbolic reasoning is difficult, when it requires executing efficient discrete operations against a large knowledge-base. In this work, we introduce a Neural Symbolic Machine, which contains (a) a neural "programmer", i.e., a sequence-to-sequence model that maps language utterances to programs and utilizes a key-variable memory to handle compositionality (b) a symbolic "computer", i.e., a Lisp interpreter that performs program execution, and helps find good programs by pruning the search space. We apply REINFORCE to directly optimize the task reward of this structured prediction problem. To train with weak supervision and improve the stability of REINFORCE, we augment it with an iterative maximum-likelihood training process. NSM outperforms the state-of-the-art on the WebQuestionsSP dataset when trained from question-answer pairs only, without requiring any feature engineering or domain-specific knowledge.

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.

In this work, we demonstrate that a simple two-layer neural network with standard activation functions can learn an arbitrary word operation in any finite group, provided sufficient width is available and exhibits grokking while doing so. To explain the mechanism by which this is achieved, we reframe the problem as that of learning a particular 3-tensor, which we show is typically of low rank. A key insight is that low-rank implementations of this tensor can be obtained by decomposing it along triplets of basic self-conjugate representations of the group and leveraging the fusion structure to rule out many components. Focusing on a phenomenologically similar but more tractable surrogate model, we show that the network is able to find such low-rank implementations (or approximations thereof), thereby using limited width to approximate the word-tensor in a generalizable way. In the case of the simple multiplication word, we further elucidate the form of these low-rank implementations, showing that the network effectively implements efficient matrix multiplication in the sense of Strassen. Our work also sheds light on the mechanism by which a network reaches such a solution under gradient descent.

Realistic use of neural networks often requires adhering to multiple constraints on latency, energy and memory among others. A popular approach to find fitting networks is through constrained Neural Architecture Search (NAS), however, previous methods enforce the constraint only softly. Therefore, the resulting networks do not exactly adhere to the resource constraint and their accuracy is harmed. In this work we resolve this by introducing Hard Constrained diffeRentiable NAS (HardCoRe-NAS), that is based on an accurate formulation of the expected resource requirement and a scalable search method that satisfies the hard constraint throughout the search. Our experiments show that HardCoRe-NAS generates state-of-the-art architectures, surpassing other NAS methods, while strictly satisfying the hard resource constraints without any tuning required.

Deep learning sometimes appears to work in unexpected ways. In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network consisting of a sequence of first-order approximations telescoping out into a single empirically operational tool for practical analysis. Across three case studies, we illustrate how it can be applied to derive new empirical insights on a diverse range of prominent phenomena in the literature -- including double descent, grokking, linear mode connectivity, and the challenges of applying deep learning on tabular data -- highlighting that this model allows us to construct and extract metrics that help predict and understand the a priori unexpected performance of neural networks. We also demonstrate that this model presents a pedagogical formalism allowing us to isolate components of the training process even in complex contemporary settings, providing a lens to reason about the effects of design choices such as architecture & optimization strategy, and reveals surprising parallels between neural network learning and gradient boosting.

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that achieve optimality. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and Neural Tangent Kernels, we provide explicit activation functions that can be used to construct networks that achieve optimality. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: (1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); (2) majority vote (model predictions are given by the label of the class with greatest representation in the training set); or (3) singular kernel classifiers (a set of classifiers containing those that achieve optimality). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful.

In this paper, we present a novel approach for incorporating external knowledge in Recurrent Neural Networks (RNNs). We propose the integration of lexicon features into the self-attention mechanism of RNN-based architectures. This form of conditioning on the attention distribution, enforces the contribution of the most salient words for the task at hand. We introduce three methods, namely attentional concatenation, feature-based gating and affine transformation. Experiments on six benchmark datasets show the effectiveness of our methods. Attentional feature-based gating yields consistent performance improvement across tasks. Our approach is implemented as a simple add-on module for RNN-based models with minimal computational overhead and can be adapted to any deep neural architecture.

Nowadays, neural networks act as a synonym for artificial intelligence. Present neural network models, although remarkably powerful, are inefficient both in terms of data and energy. Several alternative forms of neural networks have been proposed to address some of these problems. Specifically, spiking neural networks are suitable for efficient hardware implementations. However, effective learning algorithms for spiking networks remain elusive, although it is suspected that effective plasticity mechanisms could alleviate the problem of data efficiency. Here, we present a new framework for spiking neural networks - Spark - built upon the idea of modular design, from simple components to entire models. The aim of this framework is to provide an efficient and streamlined pipeline for spiking neural networks. We showcase this framework by solving the sparse-reward cartpole problem with simple plasticity mechanisms. We hope that a framework compatible with traditional ML pipelines may accelerate research in the area, specifically for continuous and unbatched learning, akin to the one animals exhibit.

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great detail. In some situations we show that neural networks learn through a process of "grokking" a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting. We also study generalization as a function of dataset size and find that smaller datasets require increasing amounts of optimization for generalization. We argue that these datasets provide a fertile ground for studying a poorly understood aspect of deep learning: generalization of overparametrized neural networks beyond memorization of the finite training dataset.

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part treatise, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct classes of algorithms, namely continuous time and discrete time models. The resulting neural networks form a new class of data-efficient universal function approximators that naturally encode any underlying physical laws as prior information. In this first part, we demonstrate how these networks can be used to infer solutions to partial differential equations, and obtain physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters.

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We formulate the neural operator as a composition of linear integral operators and nonlinear activation functions. We prove a universal approximation theorem for our proposed neural operator, showing that it can approximate any given nonlinear continuous operator. The proposed neural operators are also discretization-invariant, i.e., they share the same model parameters among different discretization of the underlying function spaces. Furthermore, we introduce four classes of efficient parameterization, viz., graph neural operators, multi-pole graph neural operators, low-rank neural operators, and Fourier neural operators. An important application for neural operators is learning surrogate maps for the solution operators of partial differential equations (PDEs). We consider standard PDEs such as the Burgers, Darcy subsurface flow, and the Navier-Stokes equations, and show that the proposed neural operators have superior performance compared to existing machine learning based methodologies, while being several orders of magnitude faster than conventional PDE solvers.

FP8 is a natural progression for accelerating deep learning training inference beyond the 16-bit formats common in modern processors. In this paper we propose an 8-bit floating point (FP8) binary interchange format consisting of two encodings - E4M3 (4-bit exponent and 3-bit mantissa) and E5M2 (5-bit exponent and 2-bit mantissa). While E5M2 follows IEEE 754 conventions for representatio of special values, E4M3's dynamic range is extended by not representing infinities and having only one mantissa bit-pattern for NaNs. We demonstrate the efficacy of the FP8 format on a variety of image and language tasks, effectively matching the result quality achieved by 16-bit training sessions. Our study covers the main modern neural network architectures - CNNs, RNNs, and Transformer-based models, leaving all the hyperparameters unchanged from the 16-bit baseline training sessions. Our training experiments include large, up to 175B parameter, language models. We also examine FP8 post-training-quantization of language models trained using 16-bit formats that resisted fixed point int8 quantization.

The approximation capability of ANNs and their RNN instantiations, is strongly correlated with the number of parameters packed into these networks. However, the complexity barrier for human understanding, is arguably related to the number of neurons and synapses in the networks, and to the associated nonlinear transformations. In this paper we show that the use of biophysical synapses, as found in LTCs, have two main benefits. First, they allow to pack more parameters for a given number of neurons and synapses. Second, they allow to formulate the nonlinear-network transformation, as a linear system with state-dependent coefficients. Both increase interpretability, as for a given task, they allow to learn a system linear in its input features, that is smaller in size compared to the state of the art. We substantiate the above claims on various time-series prediction tasks, but we believe that our results are applicable to any feedforward or recurrent ANN.

Recent advances in Neural Architecture Search (NAS) such as one-shot NAS offer the ability to extract specialized hardware-aware sub-network configurations from a task-specific super-network. While considerable effort has been employed towards improving the first stage, namely, the training of the super-network, the search for derivative high-performing sub-networks is still under-explored. Popular methods decouple the super-network training from the sub-network search and use performance predictors to reduce the computational burden of searching on different hardware platforms. We propose a flexible search framework that automatically and efficiently finds optimal sub-networks that are optimized for different performance metrics and hardware configurations. Specifically, we show how evolutionary algorithms can be paired with lightly trained objective predictors in an iterative cycle to accelerate architecture search in a multi-objective setting for various modalities including machine translation and image classification.

Algorithm learning is a core problem in artificial intelligence with significant implications on automation level that can be achieved by machines. Recently deep learning methods are emerging for synthesizing an algorithm from its input-output examples, the most successful being the Neural GPU, capable of learning multiplication. We present several improvements to the Neural GPU that substantially reduces training time and improves generalization. We introduce a new technique - hard nonlinearities with saturation costs- that has general applicability. We also introduce a technique of diagonal gates that can be applied to active-memory models. The proposed architecture is the first capable of learning decimal multiplication end-to-end.

A significant effort has been made to train neural networks that replicate algorithmic reasoning, but they often fail to learn the abstract concepts underlying these algorithms. This is evidenced by their inability to generalize to data distributions that are outside of their restricted training sets, namely larger inputs and unseen data. We study these generalization issues at the level of numerical subroutines that comprise common algorithms like sorting, shortest paths, and minimum spanning trees. First, we observe that transformer-based sequence-to-sequence models can learn subroutines like sorting a list of numbers, but their performance rapidly degrades as the length of lists grows beyond those found in the training set. We demonstrate that this is due to attention weights that lose fidelity with longer sequences, particularly when the input numbers are numerically similar. To address the issue, we propose a learned conditional masking mechanism, which enables the model to strongly generalize far outside of its training range with near-perfect accuracy on a variety of algorithms. Second, to generalize to unseen data, we show that encoding numbers with a binary representation leads to embeddings with rich structure once trained on downstream tasks like addition or multiplication. This allows the embedding to handle missing data by faithfully interpolating numbers not seen during training.

This paper explores the task of translating natural language queries into regular expressions which embody their meaning. In contrast to prior work, the proposed neural model does not utilize domain-specific crafting, learning to translate directly from a parallel corpus. To fully explore the potential of neural models, we propose a methodology for collecting a large corpus of regular expression, natural language pairs. Our resulting model achieves a performance gain of 19.6% over previous state-of-the-art models.

We introduce an algorithm where the individual bits representing the weights of a neural network are learned. This method allows training weights with integer values on arbitrary bit-depths and naturally uncovers sparse networks, without additional constraints or regularization techniques. We show better results than the standard training technique with fully connected networks and similar performance as compared to standard training for convolutional and residual networks. By training bits in a selective manner we found that the biggest contribution to achieving high accuracy is given by the first three most significant bits, while the rest provide an intrinsic regularization. As a consequence more than 90\% of a network can be used to store arbitrary codes without affecting its accuracy. These codes may be random noise, binary files or even the weights of previously trained networks.

Training a neural network is a monolithic endeavor, akin to carving knowledge into stone: once the process is completed, editing the knowledge in a network is nearly impossible, since all information is distributed across the network's weights. We here explore a simple, compelling alternative by marrying the representational power of deep neural networks with the flexibility of a database. Decomposing the task of image classification into image similarity (from a pre-trained embedding) and search (via fast nearest neighbor retrieval from a knowledge database), we build a simple and flexible visual memory that has the following key capabilities: (1.) The ability to flexibly add data across scales: from individual samples all the way to entire classes and billion-scale data; (2.) The ability to remove data through unlearning and memory pruning; (3.) An interpretable decision-mechanism on which we can intervene to control its behavior. Taken together, these capabilities comprehensively demonstrate the benefits of an explicit visual memory. We hope that it might contribute to a conversation on how knowledge should be represented in deep vision models -- beyond carving it in ``stone'' weights.

The aim of this paper is to introduce a new learning procedure for neural networks and to demonstrate that it works well enough on a few small problems to be worth further investigation. The Forward-Forward algorithm replaces the forward and backward passes of backpropagation by two forward passes, one with positive (i.e. real) data and the other with negative data which could be generated by the network itself. Each layer has its own objective function which is simply to have high goodness for positive data and low goodness for negative data. The sum of the squared activities in a layer can be used as the goodness but there are many other possibilities, including minus the sum of the squared activities. If the positive and negative passes could be separated in time, the negative passes could be done offline, which would make the learning much simpler in the positive pass and allow video to be pipelined through the network without ever storing activities or stopping to propagate derivatives.

Neural Memory Networks (NMNs) have received increased attention in recent years compared to deep architectures that use a constrained memory. Despite their new appeal, the success of NMNs hinges on the ability of the gradient-based optimiser to perform incremental training of the NMN controllers, determining how to leverage their high capacity for knowledge retrieval. This means that while excellent performance can be achieved when the training data is consistent and well distributed, rare data samples are hard to learn from as the controllers fail to incorporate them effectively during model training. Drawing inspiration from the human cognition process, in particular the utilisation of neuromodulators in the human brain, we propose to decouple the learning process of the NMN controllers to allow them to achieve flexible, rapid adaptation in the presence of new information. This trait is highly beneficial for meta-learning tasks where the memory controllers must quickly grasp abstract concepts in the target domain, and adapt stored knowledge. This allows the NMN controllers to quickly determine which memories are to be retained and which are to be erased, and swiftly adapt their strategy to the new task at hand. Through both quantitative and qualitative evaluations on multiple public benchmarks, including classification and regression tasks, we demonstrate the utility of the proposed approach. Our evaluations not only highlight the ability of the proposed NMN architecture to outperform the current state-of-the-art methods, but also provide insights on how the proposed augmentations help achieve such superior results. In addition, we demonstrate the practical implications of the proposed learning strategy, where the feedback path can be shared among multiple neural memory networks as a mechanism for knowledge sharing.

Memory footprint is one of the main limiting factors for large neural network training. In backpropagation, one needs to store the input to each operation in the computational graph. Every modern neural network model has quite a few pointwise nonlinearities in its architecture, and such operation induces additional memory costs which -- as we show -- can be significantly reduced by quantization of the gradients. We propose a systematic approach to compute optimal quantization of the retained gradients of the pointwise nonlinear functions with only a few bits per each element. We show that such approximation can be achieved by computing optimal piecewise-constant approximation of the derivative of the activation function, which can be done by dynamic programming. The drop-in replacements are implemented for all popular nonlinearities and can be used in any existing pipeline. We confirm the memory reduction and the same convergence on several open benchmarks.

Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced convergence issues due to vanishing gradient, later resolved using residual connections. Variants of these are now widely used in modern architecture. However, the computational cost of backpropagation remains a major burden, accounting for most of the training time. Taking advantage of residual-like architectural designs, we introduce Highway backpropagation, a parallelizable iterative algorithm that approximates backpropagation, by alternatively i) accumulating the gradient estimates along the residual path, and ii) backpropagating them through every layer in parallel. This algorithm is naturally derived from a decomposition of the gradient as the sum of gradients flowing through all paths and is adaptable to a diverse set of common architectures, ranging from ResNets and Transformers to recurrent neural networks. Through an extensive empirical study on a large selection of tasks and models, we evaluate Highway-BP and show that major speedups can be achieved with minimal performance degradation.

It is widely believed that a neural network can fit a training set containing at least as many samples as it has parameters, underpinning notions of overparameterized and underparameterized models. In practice, however, we only find solutions accessible via our training procedure, including the optimizer and regularizers, limiting flexibility. Moreover, the exact parameterization of the function class, built into an architecture, shapes its loss surface and impacts the minima we find. In this work, we examine the ability of neural networks to fit data in practice. Our findings indicate that: (1) standard optimizers find minima where the model can only fit training sets with significantly fewer samples than it has parameters; (2) convolutional networks are more parameter-efficient than MLPs and ViTs, even on randomly labeled data; (3) while stochastic training is thought to have a regularizing effect, SGD actually finds minima that fit more training data than full-batch gradient descent; (4) the difference in capacity to fit correctly labeled and incorrectly labeled samples can be predictive of generalization; (5) ReLU activation functions result in finding minima that fit more data despite being designed to avoid vanishing and exploding gradients in deep architectures.

The problem of automatically generating a computer program from some specification has been studied since the early days of AI. Recently, two competing approaches for automatic program learning have received significant attention: (1) neural program synthesis, where a neural network is conditioned on input/output (I/O) examples and learns to generate a program, and (2) neural program induction, where a neural network generates new outputs directly using a latent program representation. Here, for the first time, we directly compare both approaches on a large-scale, real-world learning task. We additionally contrast to rule-based program synthesis, which uses hand-crafted semantics to guide the program generation. Our neural models use a modified attention RNN to allow encoding of variable-sized sets of I/O pairs. Our best synthesis model achieves 92% accuracy on a real-world test set, compared to the 34% accuracy of the previous best neural synthesis approach. The synthesis model also outperforms a comparable induction model on this task, but we more importantly demonstrate that the strength of each approach is highly dependent on the evaluation metric and end-user application. Finally, we show that we can train our neural models to remain very robust to the type of noise expected in real-world data (e.g., typos), while a highly-engineered rule-based system fails entirely.